Bonn Topology Group - Abstracts

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Talk

January 21st 2020
Emanuele Dotto (University of Warrick, Coventry, UK): The Grothendieck-Witt theory of quadratic functors

Abstract

The Grothendieck-Witt spectrum of a ring is an object constructed from the forms (quadratic, symmetric, or symplectic) on that ring, in a way analogous to Quillen's algebraic K-theory. I will talk about joint work with B. Calmès, Y. Harpaz, F. Hebestreit, M. Land, K. Moi, D. Nardin, T. Nikolaus & W. Steimle, where we extend this construction to stable infinity categories equipped with a suitable quadratic functor, which encodes a formal notion of forms on the objects of the category. This general framework allows us to establish a general relationship between Grothendieck-Witt theory and Ranicki-Wall's L-theory generalizing a theorem of Schlichting, and settle several classical conjectures on the Grothendieck-Witt spectrum of rings.

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